This invention relates generally to phase comparison interferometer arrays utilized in the directional characterization, or direction finding, of radio frequency (RF) emitters from an observational platform. More particularly, the invention relates to the arrangement or placement of antennas in such arrays.
Interferometry is a technique for determining the direction of arrival of plane wave radio frequency signals by measuring signal path length differences from the plane wave source to two or more receiving antennas. The characterization of the r.f. signal as "plane wave" requires that the distance to the source is much greater than the distance between antennas, so the rays incident on the antennas are parallel. When this is true the observing platform is said to be in the far field of the emitter.
Antenna arrays in such devices must perform the direction finding (DF) with the needed accuracy, which requires a large spacing between the antennas. But this large spacing leads to ambiguous emitter angle-of-arrival information. Resolving the latter ambiguities requires the addition of antenna elements at precise relative antenna locations to control the gross error rate. Moreover, precise placement of the antenna elements in an interferometer array is difficult to achieve on many observational platforms, such as aircraft.
With the observer in the emitter's far field, the signals received in pairs of the interferometer's precisely placed antennas can be phase-compared and the relative phase shift will depend only on the angle-of-arrival, or AOA, and the number of signal wavelengths between the two antennas. The relationship between measured phase and AOA on the ith baseline is ##EQU1## where u is the direction-of-arrival or DOA unit vector, i.e. the signal wave normal, .theta. the AOA, and d.sub.i is the vector from one antenna element to the other, subsequently referred to simply as the ith baseline. The integer n is the "ambiguity integer", and represents the number of equally possible AOA's corresponding to the measured phase. This number is a function of both the emitter signal wavelength .lambda. and interferometer baseline length d.sub.i, e.g. if the inequality ##EQU2## is satisfied, n is equal to 0 and a unique value of measured .phi..sub.i may be associated with a single .theta.. Equation 3 shows the unambiguous field-of-view, or FOV is inversely proportional to the baseline length. Practical systems have measurement error .epsilon..sub..phi., as indicated in Equation 1, and this produces an AOA error ##EQU3## also inversely proportional to the baseline length. Equation 3 and Equation 4 establish the basic problem of interferometer design: obtaining an accurate angle estimate over a wide field-of-view given that increasing angle measurement accuracy causes the unambiguous FOV to contract.
This problem of obtaining accurate and unambiguous emitter AOA is often solved by adding additional antennas in a location collinear with the first pair. Such an antenna array is called a linear interferometer. By comparing the phase measurements made between the multiple pairs of antennas the unique AOA can be found. The process of converting multiple AOA ambiguous phase measurements into the unique, correct AOA is known as "ambiguity resolution", and performing this resolution incorrectly results in a "gross error". Linear interferometers using three or more antennas to resolve ambiguity are described in U.S. Pat. No. 3,631,496 by Fink, Burnham and Marks, and also in U.S. Pat. No. 3,852,754 by Worrell.
Robert L. Goodwin, in "Ambiguity-Resistant Three and Four--Channel Interferometers", (NRL Report 8005 Sep. 9, 1976) demonstrates that the gross error rate across the field-of-view is best controlled in linear interferometers when the antenna element spacings consist of certain integer multiples of a greatest common divisor of the antenna spacings, d.sub.0, where ##EQU4## In this equation .lambda..sub.hf is the signal wavelength at the highest frequency of interest, and AOA.sub.FOV the angular field-of-view desired.
In many phase interferometer applications direction-of-arrival, or DOA is required. DOA provides elevation and azimuth to the emitter, rather than simply the AOA cone the emitter may lie on. DOA cannot typically be provided by a single linear array in current systems, but requires noncolinear antenna elements. U.S. Pat. No. 4,638,320 by Eggert et. al. describes a class of four element interferometers with the antennas located such that two of the array baselines are orthgonal. Each baseline provides an AOA, and the two AOA cones can be intersected to get the DOA. Such an array necessarily has antenna elements that lie in a plane. Furthermore, these multiple antenna elements must bear a precise relationship to one another to control the interferometer gross error rate, as taught by N. Malloy in his 1983 IEEE ICASSP paper "Analysis and Synthesis of General Planar Interferometer Arrays". In this paper, Malloy extended Goodwin's analysis for linear arrays with a method of interferometer design applicable to both linear and planar antenna element placement, i.e the generation of both AOA and DOA. His technique utilizes the design constraints of frequency range of operation, field-of-view required, DF accuracy needed, maximum gross error rate allowed, and interacts these with the backplane available for antenna placement to determine the number of antenna elements, their diameters and the precise relative locations that must be used. For both linear and planar designs the antenna elements are separated by integer spacings (FIG. 1a, 50), which is critical in obtaining the same gross error rate at all frequencies and AOA's of interest. Thus in Malloy's approach, the multiple baselines and phase measurements given by ##EQU5## have baselines designed such that EQU D.sup.5 =PT.sup.t ( 7)
where p is an array of integers and T is a matrix analogous to d.sub..phi. in the Goodwin approach. Intrinsic to Malloy's method is the existence of another integer matrix B such that EQU BP.sup.5 =0 (8)
Generating suitable antenna placements, or D.sup.t, such that the most appropriate integer matrices P, and B result is a complex process.
Other design approaches include that of W. B. Kendall, "Unambiguous Accuracy of an Interferometer Angle-Measuring System," IEEE Trans. SET-11.62-70 (June 1965). This approach may not achieve the uniform gross error rate across the field-of-view intrinsic to the Malloy approach.
This approach, as described in the literature, and other well-established linear and planar design techniques, does not generate arrays using antenna elements mounted on curved surfaces. They are concerned with the precise placement of antenna elements on a common ground plane. This is a significant drawback for two reasons. The aircraft surfaces the interferometer is mounted on are generally curved to reduce drag and increase structural integrity. Use of a common ground plane means planar or linear interferometer designs must be mounted behind curved radomes. These radomes have broadband r.f. transmission limitations that cause them to be major sources of phase measurement error. Antenna manufacturing techniques have advanced to the production of elements that fit conformably to the surface they are mounted on, thus eliminating the need for radomes.
Also, when applying these established design techniques to interferometers mounted on aircraft, it is frequently difficult to find space to place the antennas in their required precise relative positions. For this reason compromise is typically made that degrades FOV, DF accuracy, gross error rate or other significant performance requirements. The desired DOA accuracies are typically not achieved because of constraints on antenna size and number.